The main originality that Prigogine portrays is the way in which he sees
the introduction of probabilities in the dynamical description of an unstable
system (with persistent interactions). In classical dynamics this is seen as a
measure of our ignorance of the system. In fact, as Prigogine recognises, “the
equations of chaotic systems are deterministic” (p. 32)[i],
which means that, the unpredictable character of the behaviour of unstable (or
even chaotic) systems is due to the finite precision with which we can describe
the initial conditions. Therefore, the unpredictability is seen as a
characteristic of the description and
not of the system itself.

On the other hand, some unstable systems, for instance the ones in which
Poincaré resonances appear, are unpredictable because the trajectories in these
systems are impossible to calculate (thus, infinite precision in the
description of the initial conditions would not help). Like Prigogine says, in
the classical interpretation this is still viewed as deriving from a lack of
information: “any dynamical system must follow a trajectory, solution of its
equations, disregarding the fact that we can reach them or not.” (p. 41)

Opposing this interpretation, Prigogine questions our reasons for
supposing that trajectories are elementary entities. Instead, he proposes that
probability waves or distributions should be seen as the elementary entities
from which trajectories arise:

“But this [the
trajectory] ceases to be an elementary
concept in the statistical description. In this case, to obtain a trajectory,
we should concentrate the distribution of probabilities in a single point. …
The trajectory becomes the result of a physical-mathematical construction.” (p.
118)

There are at least three reasons advanced for this change in
perspective: the first is because, in unstable systems, the description based
on trajectories is not as complete as the statistical description. The latter,
Prigogine argues, gives more complete and accurate predictions, especially
because it includes non-local
interactions,[ii] which is
impossible for the trajectory description to account for. The second reason has
to do with the introduction of the arrow of time in the microscopic laws of
physics, thus eliminating the inconsistency between our theories and
observations (according to our mechanical theories there should be no
privileged direction of time). The third reason is that it allows for a realist
interpretation of quantum mechanics.

But Prigogine’s proposal has to deal at least with two serious
difficulties. The first one is to give a physical meaning to the probability
distributions. Usually probability distributions are seen as theoretical
concepts, how can they create or destroy physical things like electrons or
photons? The second is that Prigogine, when saying that the statistical level
can make better predictions (regarding unstable systems) than the ones based on
trajectories, is using incomplete
trajectory descriptions. Although this is not a problem if we want to speak of
the theories we use, it certainly
becomes one if we want to speak of the way the world is.

Anyway this last objection only shows that classical interpretation of
dynamics is still defensible; the plausibility of Prigogin’s proposal will more
strongly depend on whether we can conceive (non-physical) probabilities, or (popperian) propensities, as elementary entities, and the way in which a
particular possibility is selected or actualised. A problem whose solution is
inextricably connected with the lines that frame the philosophical mind-body
problem since at least Descartes.

[i] All the quotes and page references were translated/taken from the
portuguese edition of La Fin des
Certitudes.

[ii] And also because it includes a description of the phase state: “So,
it contains an additional information,
which is lost in the description of individual trajectories.” (p.37)